Algebraic Logic
Which algebraic structures let us describe logical states and operations consistently?
The research idea
B-Theory’s algebraic-logic line explores Boolean modules and logical state vectors, including the proposed language of Bectors. These are attempts to put logical expressions in a form that supports explicit operations, comparison, and calculation.
The CM/LM operator calculus is the current paper-backed anchor for part of this programme. It gives exact relationships between formula-valued and numeric Boolean operators. Its scope should not be taken to establish every wider claim once associated with Bectors or a general algebraic theory of mind.
Why it matters
Mathematical questions about observation and change need a well-defined state space. This project asks what representations are appropriate before moving to observation topologies or concept differentiation.
Open work
A useful next research direction is to state exactly which Bector constructions add capabilities beyond established Boolean-module and truth-vector methods, then give examples and limitations. This page serves as the programme-level home for that question.